platt
flat
Level, flat, and without elevations.
Die Landschaft hier ist völlig platt, es gibt keine Hügel.
The landscape here is completely flat; there are no hills.

flat / exhausted
Loading your saved state.
flat
Level, flat, and without elevations.
Die Landschaft hier ist völlig platt, es gibt keine Hügel.
The landscape here is completely flat; there are no hills.

The basic meaning 'flach' (flat) is neutral. However, the figurative meanings such as 'erschöpft' (exhausted), 'erstaunt' (amazed), or 'niveaulos' (lowbrow) are colloquial and should not be used in formal contexts.
Die Pfannkuchen müssen schön dünn und platt sein.
The pancakes need to be nice and thin and flat.
In the meaning 'erschöpft' (exhausted), 'platt' is used only predicatively, that is, after a verb like 'sein' (to be). You cannot say 'ein platter Mensch' if you mean that the person is tired.
Ich gehe heute früh ins Bett, ich bin einfach nur platt.
I'm going to bed early today; I'm just exhausted.
In connection with a tire, the colloquial expression 'einen Platten haben' (to have a flat) is very common. Here, the adjective is used as a noun: 'der Platte'.
Wir müssen anhalten, ich glaube, wir haben einen Platten.
We need to stop; I think we have a flat.
When someone is 'platt' (stunned), it can also mean that he or she is speechless with surprise. Here too, the word is used only predicatively, often with 'sein' (to be) or 'machen' (to make).
Seine Reaktion hat mich echt platt gemacht.
His reaction really stunned me.
When something is described as 'platt' (corny/crude), it is unoriginal or primitive. Typical combinations are 'ein platter Witz' (a corny joke), 'ein platter Spruch' (a corny remark), or 'eine platte Ausrede' (a lame excuse).
Er versucht immer, mit platten Komplimenten Eindruck zu machen.
He always tries to make an impression with corny compliments.
When referring to the dialect, 'Platt' can be used like a noun without an article. You say 'Platt sprechen' (to speak Low German) or 'etwas auf Platt sagen' (to say something in Low German).
An der Küste können noch viele alte Leute Platt sprechen.
On the coast, many older people can still speak Low German.
just / exactly
'eben' and 'platt' can both describe something that is flat and has no raised areas. 'eben' sounds more neutral and works well when a surface is smooth or level, for example a floor or a path. 'platt' often sounds a bit more colloquial or stronger, and tends to mean that something has been pressed completely flat. For a normal, level surface, 'eben' is usually more natural. When something has been flattened or seems very flat, 'platt' fits better.

Nach dem Umzug war der Karton ganz platt.
After the move, the box was completely flat.
Der Weg am See ist eben und gut für Kinderwagen geeignet.
The path by the lake is level and suitable for strollers.